A polynomial, p(x)=3x^4+Bx^3+Cx^2+x-2, has real coefficients. a. Show that P(x) has at least one positive and one negative real zero. b. Given that one of the zeros of P(x) is -4/3, what can we say for certain about B(the x^3 coefficient) and C (the x^2 coefficient?

A polynomial, p(x)=3x^4+Bx^3+Cx^2+x-2, has real coefficients. a. Show that P(x) has at least one positive and one negative real zero. b. Given that one of the zeros of P(x) is -4/3, what can we say for certain about B(the x^3 coefficient) and C (the x^2 coefficient?

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.5: Complex Zeros And The Fundamental Theorem Of Algebra

Problem 3E: A polynomial of degree n I has exactly ____________________zero if a zero of multiplicity m is...

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Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

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6. A polynomial, p(x)=3x^4+Bx^3+Cx^2+x-2, has real coefficients.

a. Show that P(x) has at least one positive and one negative real zero.

b. Given that one of the zeros of P(x) is -4/3, what can we say for certain about B(the x^3 coefficient) and C (the x^2 coefficient?

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